According to the Wall Street Journal, AB InBev currently owns a 50-percent non-controlling stake in Modelo, Mexico's largest brewer. While there is not concrete timeline for a deal, two people familiar with the talks told the news outlet that it could come as early as this week. It is also possible that the talks could break down before any deal is reached, it added.

Modelo, which traces its roots back to 1925, has a market value equivalent to $23 billion. Its brands -- which include Corona Extra, Corona Light, Modelo Especial and Victoria -- are imported into the United States and marketed through a joint venture the company has with U.S. wine and spirits maker Constellation Brands Inc.

Spokeswomen for AB InBev and Modelo declined to comment for the WSJ's report.

The two companies have had some problems in the past. According to the news report, AB InBev inherited the 50-percent stake in its $52-billion acquisition of Budweiser maker Anheuser-Busch in 2008, which created the world's largest beer maker by sales. Anheuser had tried unsuccessfully to entice Modelo to merge with the U.S. brewing giant after it received the unsolicited approach from InBev, people familiar with the matter said at the time.

After InBev sealed the Anheuser-Busch deal, Modelo claimed that Anheuser-Busch breached a prior agreement between the two companies by failing to consult the Mexican company on its sale to InBev. In 2010, an arbitration panel ruled in favor of the merged company, AB InBev, ending the dispute and, according to analysts at the time, paving the way for AB InBev to eventually consolidate its ownership of Modelo, the WSJ reported.